Provided is a second part composition for hair dyeing or bleaching, which is mixed with a first part composition containing an alkali agent before use, the composition containing the following components (A) to (D): (A) an organic amine having at least one hydrophobic chain or a salt thereof; (B) an oily component which is a liquid form at 25° C. under normal pressure (1013.25 hPa); (C) an oxidizing agent; and (D) water, in which the composition has a pH of 1 to 6 at 25° C.